Witnessing Nonclassicality in a Causal Structure with Three Observable Variables

Seen from the modern lens of causal inference, Bell's theorem is nothing other than the proof that a specific classical causal model cannot explain quantum correlations. It is thus natural to move beyond Bell's paradigmatic scenario and consider different causal structures. For the specific case of three observ-able variables, it is known that there are three nontrivial causal networks. Two of those are known to give rise to quantum nonclassicality: the instrumental and the triangle scenarios. Here we analyze the third and remaining one, which we name the Evans scenario, akin to the causal structure underlying the entanglement-swapping experiment. We prove a number of results about this elusive scenario and introduce new and efficient computational tools for its analysis that can also be adapted to deal with more general causal structures. We do not solve its main open problem-whether quantum nonclassical correlations can arise from it-but give a significant step in this direction by proving that postquantum correlations, analogous to the paradigmatic Popescu-Rohrlich box, do violate the constraints imposed by a classical description of the Evans causal structure.

Automated summary

Seen from the modern lens of causal inference, Bell's theorem proves that a specific classical causal model cannot explain quantum correlations. Therefore, it is necessary to consider different causal structures. For the case of three observable variables, there are three nontrivial causal networks, and we analyze the third one, named the Evans scenario, which is similar to the causal structure underlying the entanglement-swapping experiment. We introduce new computational tools and prove that postquantum correlations violate the constraints imposed by a classical description of the Evans causal structure.